Rešite frac{(3a^{5})^{2}}{(2b^{4})^{3}}:(9a^3)^2/(8b^5)^3

$$\frac { ( 3 a ^ { 5 } ) ^ { 2 } } { ( 2 b ^ { 4 } ) ^ { 3 } } : \frac { ( 9 a ^ { 3 } ) ^ { 2 } } { ( 8 b ^ { 5 } ) ^ { 3 } }$$

Ovrednoti

$$\frac{64b^{3}a^{4}}{9}$$

Koraki rešitve

Delite \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} s/z \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} tako, da pomnožite \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} z obratno vrednostjo \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.

$$\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(3a^{5}\right)^{2}.

$$\frac{3^{2}\left(a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 5 in 2, da dobite 10.

$$\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Izračunajte potenco 3 števila 2, da dobite 9.

$$\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(8b^{5}\right)^{3}.

$$\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 5 in 3, da dobite 15.

$$\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Izračunajte potenco 8 števila 3, da dobite 512.

$$\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Pomnožite 9 in 512, da dobite 4608.

$$\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(2b^{4}\right)^{3}.

$$\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 4 in 3, da dobite 12.

$$\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}$$

Izračunajte potenco 2 števila 3, da dobite 8.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(9a^{3}\right)^{2}.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 3 in 2, da dobite 6.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}$$

Izračunajte potenco 9 števila 2, da dobite 81.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}$$

Pomnožite 8 in 81, da dobite 648.

$$\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}$$

Okrajšaj 72a^{6}b^{12} v števcu in imenovalcu.

$$\frac{64b^{3}a^{4}}{9}$$

Razširi

$$\frac{64b^{3}a^{4}}{9}$$

Koraki rešitve

Delite \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} s/z \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} tako, da pomnožite \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} z obratno vrednostjo \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.

$$\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(3a^{5}\right)^{2}.

$$\frac{3^{2}\left(a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 5 in 2, da dobite 10.

$$\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Izračunajte potenco 3 števila 2, da dobite 9.

$$\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(8b^{5}\right)^{3}.

$$\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 5 in 3, da dobite 15.

$$\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Izračunajte potenco 8 števila 3, da dobite 512.

$$\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Pomnožite 9 in 512, da dobite 4608.

$$\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(2b^{4}\right)^{3}.

$$\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 4 in 3, da dobite 12.

$$\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}$$

Izračunajte potenco 2 števila 3, da dobite 8.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}$$

Razčlenite \left(9a^{3}\right)^{2}.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 3 in 2, da dobite 6.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}$$

Izračunajte potenco 9 števila 2, da dobite 81.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}$$

Pomnožite 8 in 81, da dobite 648.

$$\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}$$

Okrajšaj 72a^{6}b^{12} v števcu in imenovalcu.

$$\frac{64b^{3}a^{4}}{9}$$